The 29-year-old Brit has never been past the semi-finals at the season-ending event.
Murray has never been past the semi-finals at the season-ending event, but the Scot arrives at London's O2 Arena with a huge incentive to take the title.
The 29-year-old shattered Novak Djokovic's 122-week reign at top of the world rankings over the weekend by reaching the final of the Paris Masters.
To ensure his first taste of the number one position lasts more than two weeks, Murray must match or better Djokovic's performance at the Tour Finals, a tournament the Serb has won for the past four years.
After toasting his success while flying back to London on a private jet after winning the Paris Masters on Sunday, Murray was back to business on Monday as he learned his initial opponents in the Tour Finals.
Murray has had mixed results against his group rivals this year, losing to Japan's Nishikori in the US Open quarter-finals after beating him at the Rio Olympics and in the Davis Cup.
He has lost three of his past four matches against world number three Wawrinka, including in last year's group stage, although he did beat the Swiss in their only meeting this year in the French Open semi-finals.
Murray was also beaten by former US Open champion Cilic in their last meeting, in the Cincinnati final, but he defeated the Croatian in the Queen's Club semi-finals in June.
After winning Wimbledon for a second time and then taking the second Olympic singles gold of his career, Murray can cap a dream year by lifting the Tour Finals trophy.
"Yesterday was a great day, today has just been a normal day at home with the family," said Murray, whose first match of the Tour Finals will be against Cilic next Monday.
"Once you're out on the court you don't think about your ranking. You're playing against the top eight players in the world. I look forward to getting out there and playing at the O2.
"I'll try and take a few days rest now, start hitting again on Thursday. I need a few days' break.
"It will be one big push for all the guys. Everyone has played a lot of tennis and hopefully everyone can play well."
After looking invincible in the first half of the year, Djokovic, who faces Milos Raonic, Gael Monfils and Dominic Thiem in the other group, suddenly finds himself playing second fiddle to Murray.
The reigning Australian and French Open champion will play in the first match of the Tour Finals on Sunday against rising Austrian star Thiem.
Draw for the ATP World Tour finals group stage made in London on Monday (x denotes seeding):
Andy Murray (GBR x1)
Stan Wawrinka (SUI x3)
Kei Nishikori (JPN x5)
Marin Cilic (CRO x7)
Novak Djokovic (SRB x2)
Milos Raonic (CAN x4)
Gael Monfils (FRA x 6)
Dominic Thiem (AUT x8)